The piece is for playing guitar using plectrum:
I am guessing the horizontal line represents the stretch of notes to be played at the changed tempo, and begin playing at the initial tempo after that.
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Just curious, what is the name/author of this piece? – Jürgen Apr 30 '19 at 21:26
This line refers to the I, not to the "Allegro".
As OP mentioned in the comments, the I stands for the first position, i. e. the first fret on the guitar. So the line means, that all notes under it have to be played in the first position.
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This very nearly reads as if all the notes are played on the first fret ! A little more information would help beginners especially, even though lots of readers seem to like the answer. – Tim Apr 26 '19 at 6:54
Not associated with the time change, just coincidental. On guitar music, there's often a Roman numeral printed to suggest a good position on the neck to play that section. Here, it's the scale of the F Mixolydian mode, starting from 1st fret bottom string. So a sensible position to play all the notes would be starting o that very fret. Although, promoting an open A on the 5th string somewhat negates the 'I'. Not a lot of point in putting it, in my opinion.
That looks like guitar music (single staff, G clef, Arabic numbers that make sense for guitar fingerings). If so...
It gives you the position that passage is to be played in
The Bb note in the preceding measure can't be played on any of the five lowest frets. Given the fingering for that note and the ones that follow, the music is indicating third position there: G with the first finger/3rd fret, Eb ad Ab with the second finger/4th fret, F and Bb with the fourth finger/6th fret.
There's no finger number indicated for the Eb at the start of the measure you're questioning. But the second note, F below the staff, can't be played in third position, so it's going to require a shift. The music is telling you to shift ON the F, rather than shifting earlier in preparation for the F.
Guitar positions are traditionally marked with Roman numerals. That F is playable in either first or second position - the music is telling you to do it in first.
Position marks are usually preceded with "C" (Italian for capotasto, fret) to avoid confusion with Roman numerals from analysis. But not all publishers do that.
The horizontal line tells you all the notes under it are to be played in first position. It ends at the Bb; the C that follows could be played in either first or second position, so it's your choice.
As a guitarist, it's a little odd that the publisher chose to mark the position for that passage. Since there aren't many choice for how to play the F, and they also provide finger numbers, it's already obvious that passage is in first position. And they didn't mark the measure below - from the fingering, beat 1 is first position, beats 2 & 3 are second position, and beat 4 is fourth position. But sometimes publishers/composers do odd things.
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1'There aren't many choices for how to play the F.' Are there any other choices at all? I agree that the line above, and that below, could do with position numbers, far more than the 'I'. – Tim Apr 25 '19 at 11:10
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It's true that it's only playable on the 6th string, first fret. But that's available in two positions. In all positions on the guitar above the first you can only play in two keys without reaching for at least one note, and you can reach forward or back. So this passage is playable in first position (as written) or second position (with stretches for F, the lower Bb, and the Eb). In second position you can actually play the lower Bb and Eb in two different ways, depending on whether you stretch up or down - the guitar is an incredibly flexible instrument for fingering choices. – Tom Serb Apr 25 '19 at 13:18
